An explicit analytical solution is derived for sloshing in a cylindrical liquid storage tank with a single-deck type floating roof under seismic excitation. The floating roof is composed of an inner deck, which may be idealized as an isotropic elastic plate with uniform thickness and mass, and connected to an outer pontoon, which can be modeled as an elastic curved beam. The contained liquid is assumed to be inviscid, incompressible, and irrotational. By expanding the response of the floating roof into free-vibration modes in air and applying the Fourier–Bessel expansion technique in cylindrical coordinates, the solution is obtained in an explicit form, which is exact within the framework of linear potential theory. Numerical results are presented to investigate the effect of the type (single-deck or double-deck) and stiffness of the floating roof on the sloshing response.

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